Abstract
A physically based model for auotgenous shrinkage and swelling of portland cement paste is necessary for computation of long-time hydgrothermal effects in concrete structures. The goal is to propose such a model. As known since 1887, the volume of cement hydration products is slightly smaller than the original volume of cement and water (chemical shrinkage). Nevertheless, this does not imply that the hydration reaction results in contraction of the concrete and cement paste. According to the authors’ recently proposed paradigm, the opposite is true for the entire lifetime of porous cement paste as a whole. The hydration process causes permanent volume expansion of the porous cement paste as a whole, due to the growth of C–S–H shells around anhydrous cement grains which pushes the neighbors apart, while the volume reduction of hydration products contributes to porosity. Additional expansion can happen due to the growth of ettringite and portlandite crystals. On the material scale, the expansion always dominates over the contraction, i.e., the hydration per se is, in the bulk, always and permanently expansive, while the source of all of the observed shrinkage, both autogenous and drying, is the compressive elastic or viscoelastic strain in the solid skeleton caused by a decrease of chemical potential of pore water, along with the associated decrease in pore relative humidity. As a result, the selfdesiccation, shrinkage and swelling can all be predicted from one and the same unified model, in which, furthermore, the low-density and high-density C–S–H are distinguished. A new thermodynamic formulation of unsaturated poromechanics with capillarity and adsorption is presented. The recently formulated local continuum model for calculating the evolution of hydration degree and a new formulation of nonlinear desorption isotherm are important for realistic and efficient finite element analysis of shrinkage and swelling. Comparisons with the existing relevant experimental evidence validate the proposed model.
Highlights
Introduction and objectiveIt is usually required that concrete structures such as bridges be designed for a lifespan of at least hundred years
The present analysis shows that the autogenous shrinkage and swelling evolve logarithmically for decades, and probably even for centuries
Already in 1887, Le Chatelier showed that the cement hydration reaction is always contractive, i.e., the volume of the cement gel produced by hydration is always smaller than the sum of the original volumes of anhydrous cement and water
Summary
It is usually required that concrete structures such as bridges be designed for a lifespan of at least hundred years. The general form of such a model was proposed in Bazant et al [4] and was developed in more detail in Bazant et al [5] In this study, this previous model is refined, put on a solid thermodynamic basis, and made comprehensive so that it would agree with all the basic types of experiments reported in the literature. This previous model is refined, put on a solid thermodynamic basis, and made comprehensive so that it would agree with all the basic types of experiments reported in the literature 2. Long-time drying shrinkage tests for specimens of various sizes, in which the autogenous shrinkage is under way in the core until the drying front arrives. The analysis that follows recognizes that data fitting must employ realistic models for: (1) creep [7], (2) hydration [8], (3) moisture diffusion [9], and (4) cracking damage due to tensile stresses caused, e.g., by drying shrinkage (for 2 and 3, see ‘‘Appendices 1 and 2’’)
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